Altitude estimation using differential pressure sensors in ground effect

ABSTRACT

A plurality of sensor datasets is received including: (1) an interference sensor dataset which is associated with interference between airflow from a first rotor in a multicopter and airflow from a second rotor in the multicopter, (2) a first and a second isolated sensor dataset which are associated with isolated airflows from the first rotor and the second rotor, respectively. A generalized flow model associated with a generalized rotor is received and an altitude for the multicopter is generated based at least in part on the plurality of sensor datasets and the generalized flow model, including by using a non-linear filter that builds a consolidated probability function associated with altitude that reconciles the plurality of sensor datasets with the generalized flow model.

CROSS REFERENCE TO OTHER APPLICATIONS

This application is a continuation of co-pending U.S. patent applicationSer. No. 16/507,859 entitled ALTITUDE ESTIMATION USING DIFFERENTIALPRESSURE SENSORS IN GROUND EFFECT filed Jul. 10, 2019 which isincorporated herein by reference for all purposes.

BACKGROUND OF THE INVENTION

Accurate estimation of an aircraft's position in the air (e.g.,altitude, attitude, etc.) is very important. Some current altitudeestimation techniques rely upon vision or wave-based propagationtechniques, such as radar and Lidar. However, vision and wave-basedaltitude estimation techniques are undesirable in some applications fora variety of reasons. For example, vision and wave-based altitudeestimation techniques do not sense the presence of ground effect and sowould not work well for vertical takeoff and landing (VTOL) multicopters(which generate large amounts of downward airflow) when such aircraftare operating near the ground. The downward airflow acts as a cushionbetween the vehicle and the ground and contributes to abnormal vehicledynamics, hence methods that accurately sense the interaction between amulticopter and the ground are crucial for successful VTOL. Anotherdrawback to wave-based altitude estimation techniques is that wave-basedsystems tend to be heavy and/or expensive. New altitude estimationtechniques which work in the presence of ground effect and/or which arerelatively light and/or inexpensive would be desirable (e.g., for use inlightweight and/or VTOL multicopters).

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of the invention are disclosed in the followingdetailed description and the accompanying drawings.

FIG. 1A is a flowchart illustrating an embodiment of a process togenerate an altitude for a multicopter.

FIG. 1B is a diagram illustrating an embodiment of a system whichgenerates an altitude for a multicopter.

FIG. 2 is a diagram illustrating an embodiment of an ultralight andoverwater multicopter.

FIG. 3 is a diagram illustrating a top view of a multicopter with therotors on.

FIG. 4 is a diagram illustrating an embodiment of ground effect airflowwith induced velocity sensor datasets used as inputs to the flow model.

FIG. 5A is a diagram illustrating a first side view of an embodiment ofa sensor that includes differential pressure probes.

FIG. 5B is a diagram illustrating a second side view of an embodiment ofa sensor that includes differential pressure probes.

FIG. 6A is a three-dimensional graph illustrating an embodiment of ageneralized flow model with the rotor at a first height.

FIG. 6B is a two-dimensional graph illustrating an embodiment of ageneralized flow model with the rotor at a first height.

FIG. 6C is a two-dimensional graph illustrating an embodiment of ageneralized flow model with the rotor at a second height.

FIG. 7A is a graph illustrating an embodiment of a consolidatedprobability function, comprising a prior probability density function,at a first point in time.

FIG. 7B is a graph illustrating an embodiment of a likelihood functionwhich is constructed using sensor data and the generalized flow model.

FIG. 7C is a graph illustrating an embodiment of a posterior functionwhich is constructed from a likelihood function and a prior function.

FIG. 7D is a graph illustrating an embodiment of a predicted function.

FIG. 8 is a diagram illustrating an embodiment of a process to generatean altitude for a multicopter where a consolidated probability functionis updated over time.

FIG. 9 is a diagram illustrating an embodiment of a process to generatean altitude and an attitude for a multicopter.

FIG. 10 is a diagram illustrating an embodiment of ground effect airflowwhen there is a non-zero attitude.

DETAILED DESCRIPTION

The invention can be implemented in numerous ways, including as aprocess; an apparatus; a system; a composition of matter; a computerprogram product embodied on a computer readable storage medium; and/or aprocessor, such as a processor configured to execute instructions storedon and/or provided by a memory coupled to the processor. In thisspecification, these implementations, or any other form that theinvention may take, may be referred to as techniques. In general, theorder of the steps of disclosed processes may be altered within thescope of the invention. Unless stated otherwise, a component such as aprocessor or a memory described as being configured to perform a taskmay be implemented as a general component that is temporarily configuredto perform the task at a given time or a specific component that ismanufactured to perform the task. As used herein, the term ‘processor’refers to one or more devices, circuits, and/or processing coresconfigured to process data, such as computer program instructions.

A detailed description of one or more embodiments of the invention isprovided below along with accompanying figures that illustrate theprinciples of the invention. The invention is described in connectionwith such embodiments, but the invention is not limited to anyembodiment. The scope of the invention is limited only by the claims andthe invention encompasses numerous alternatives, modifications andequivalents. Numerous specific details are set forth in the followingdescription in order to provide a thorough understanding of theinvention. These details are provided for the purpose of example and theinvention may be practiced according to the claims without some or allof these specific details. For the purpose of clarity, technicalmaterial that is known in the technical fields related to the inventionhas not been described in detail so that the invention is notunnecessarily obscured.

Various embodiments of techniques to measure, estimate, or otherwisegenerate an altitude associated with a multicopter are described herein.As used herein, the term multicopter refers to an aircraft with multiplerotors that rotate about a vertical axis of rotation. This configurationof rotors (e.g., which generates airflow downwards) permits amulticopter to perform vertical takeoff and landings (VTOL).

In some applications, the multicopter is an ultralight (e.g., weighingon the order of 250 pounds) and is flown autonomously. One problem withautonomous ultralight multicopters is that it is important to get anaccurate estimate or measurement of the altitude. For example, during anautonomous vertical landing (e.g., where there is no pilot to visuallygauge the distance to the ground and adjust the multicopter's verticaldescent accordingly), an inaccurate altitude estimate or measurementcould lead to an uncomfortable or even dangerous landing if theautonomous flight controller thinks the multicopter is higher off theground than it is. With a pilot, a less accurate altitude estimator maybe sufficient because the pilot will observe the vehicle's altitude andrespond accordingly (e.g., slow the vehicle's descent just prior totouching down during a vertical landing). As will be described in moredetail below, the various estimation techniques described herein producesufficiently accurate results and are suitable for implementation in aprocessing and/or storage resource-limited environment and/or anultralight application (e.g., since an ultralight will typically havemoderate processing and storage resources available for altitudeestimation, given the severe weight restrictions of an ultralight).

The nature of the multicopter lies in its multiple rotors, whichcontribute to a large effective rotor diameter, that is, the maximumtip-to-tip distance between the most outboard rotors (e.g., the maximumdistance between the left front outboard rotor tip and right frontoutboard rotor tip in the example 10-rotor multicopter described below).Since ground effect is present when operating at a height equivalent tothe effective rotor diameter, the multicopter could be operating inground effect during a large portion of a flight, hence making accuratesensing and estimation of ground effect even more important.

FIG. 1A is a flowchart illustrating an embodiment of a process togenerate an altitude for a multicopter. In various embodiments, theexemplary process described here is performed by a variety ofcomponents, modules, and/or devices on a multicopter, such as a computerprogram product (e.g., embodied in a non-transitory computer readablestorage medium and comprising computer instructions), a processor and amemory (e.g., where the memory is coupled with the processor and isconfigured to provide the processor with instructions which are executedby the processor), and/or a semiconductor device (e.g., afield-programmable gate array (FPGA) or an application-specificintegrated circuit (ASIC)).

At 100, a plurality of sensor datasets including: (1) an interferencesensor dataset which is associated with interference between airflowfrom a first rotor in a multicopter and airflow from a second rotor inthe multicopter, (2) a first and a second isolated sensor dataset whichare associated with isolated airflows from the first rotor and thesecond rotor, respectively, is received. As the name implies, a sensordataset is a set of data that is received from a sensor.

At step 100, two types of sensor datasets are received: an interferencesensor dataset and an isolated sensor dataset. Interference sensordatasets are (generally speaking) sets of data associated with (e.g.,are measurements of or from) interfering (e.g., combined, mixed, etc.)airflows from two different rotors. For example, in one exemplarymulticopter described below, there are 10 rotors which are tightlypacked, sometimes so much so that two adjacent rotors overlap with eachother in a vertical direction but at different heights. In one example,a sensor is placed beneath such a rotor overlap and the data from thatsensor comprises an interference sensor dataset.

Conceptually, the interference sensor dataset provides insight into theinfluence that one rotor imparts on other rotors, which is important fora multicopter especially in the presence of ground effect. For the caseof a single rotor close to a ground plane, the increase of thrust andother deviations from nominal flow conditions are caused by interactionbetween the single rotor and ground. Due to the complex flow interactionbetween multiple rotors in a multicopter, deviations from nominal flowconditions can also be caused by ground effect and the influence fromother rotors (e.g., one rotor is spinning faster than a second rotor andthe vehicle is tilted at an angle, i.e., not horizontal).

Using the interference sensor dataset, a processor can separate theinfluence of multi-rotor interference from ground effect. One such usecase is the condition where the interference sensor dataset showsextremely noisy data, which correlates with the amount of interferencebeing roughly equivalent between rotors, as opposed to the interferencesensor dataset showing airflow being dominant from one side, whichcorresponds to one rotor spinning much faster than the other rotors andhence its airflow being dominant even in the presence of a ground plane(i.e., ground effect). Without such a dataset, the estimator would beincorrectly inferring that deviations from nominal airflow conditionsare all due to ground effect and ignore rotor flow differences.

The second type of sensor dataset received at step 100 is an isolatedsensor dataset. As the name implies, such datasets are associated with(e.g., are measurements of or from) isolated airflow (e.g., with littleor no interfering airflow from another rotor). In one example, a sensoris placed beneath a given rotor far away from other rotors and/or otherpotential sources of interference (e.g., away from large parts of themulticopter, such as a fuselage, a float, etc. which can interfere withthe airflow produced by the rotor).

At 102, a generalized flow model associated with a generalized rotor isreceived. Generally speaking, a flow model is a model of the velocityvariation across the airflow produced by a rotor when the rotor is atvarious altitudes (e.g., heights from the ground) and the rotor isspinning at various speeds. In some embodiments, the generalized flowmodel uses (e.g., as an input of the flow model) the same types ofinformation as the isolated sensor datasets received at step 100.

For example, if the isolated sensor datasets received at step 100 (e.g.,airflow) measure velocity in an isolated region at appropriate locationsbelow a first and second rotor, then the generalized flow model may havethose velocities as outputs and an induced (e.g., airflow) velocity(e.g., above and/or entering the rotor in a downward direction) as theinput to the model from the isolated sensor datasets. Another version ofthis example has a similar setup with the rotational speed of the rotorbeing used as the input to the model, where the rotational speed of therotor is mapped and/or correlated to the induced velocity of the rotor.This setup has the advantage of requiring fewer sensors since rotationalspeed of the rotor is typically already part of the multicopter rotorspeed control setup.

A generalized flow model is generalized in the sense that it isindependent of and/or agnostic to a specific rotor at a specificlocation or position in the multicopter. For example, in the actualmulticopter, the rotors will produce different airflow depending upontheir location relative to the ground and/or nearby sources ofinterference (e.g., parts of the multicopter that interfere with theairflow, other airflow from other rotors that interfere with theobserved airflow, etc.). For example, an outboard rotor that is at thedistal end of a boom and located next to three adjacent (andinterfering) rotors will produce a different airflow compared to aninboard rotor that is located over a float and is adjacent to thefuselage. Similarly, even an inboard middle rotor may have a differentairflow than an inboard front rotor or inboard back rotor due todifferent numbers, types, and/or positions of sources of interference.However, instead of obtaining multiple flow models for each rotorposition or location, a (e.g., single) generalized flow model is usedwhich is representative of a generalized rotor. For example, the(conceptual) generalized rotor may have no nearby sources ofinterference and therefore produces a clean, isolated, and/or idealairflow. This may be attractive in a resource-limited aircraft becauseonly a single flow model needs to be stored, ingested, and processed(e.g., instead of storing and using multiple flow models, each specificto a different rotor location or position).

At 104, an altitude (e.g., estimation) for the multicopter is generatedbased at least in part on the plurality of sensor datasets (e.g.,received at step 100) and the generalized flow model (e.g., received atstep 102), including by using a non-linear filter that builds aconsolidated probability function associated with altitude thatreconciles the plurality of sensor datasets with the generalized flowmodel. The consolidated probability function term is so named becausesensor data associated with various (combinations of) rotors (e.g., justthe first rotor, just the second rotor, a combination of the first rotorand the second rotor, etc.) and various (combinations of) sensordatasets associated with each rotor (e.g., just one sensor dataset frommiddle “inboard” rotors with more interference, multiple sensor datasetsat various locations relative to the front “outboard” rotor with lessinterference, etc.) is consolidated or otherwise combined into a singleprobability function. In some embodiments where altitude estimation isthe only goal, the consolidated probability function is atwo-dimensional probability density function where the x-axis is thevarious possible altitudes (i.e., heights) of the multicopter and they-axis is the corresponding probability for those various altitudes.

In building the consolidated probability function, the non-linear filterreconciles the plurality of sensor datasets with the generalized flowmodel. As described above, the generalized flow model is generalized andis not specific to one particular rotor at a particular location orposition in the multicopter (e.g., the generalized flow model reflects aclean, isolated, and/or ideal airflow). However, the various sensordatasets may display certain airflow characteristics that are reflectiveof nearby sources of interference (e.g., adjacent rotors, nearby floatsor fuselages, etc.). For example, when two rotors are close to eachother (possibly overlapping), the airflow will not be a clean “skirt”when close to the ground but will rather have some airflow distortion ator near the airflow interface between the two rotors. The generalizedflow model will reflect the interference sources as measured by thesensor datasets, and the non-linear filter further reconciles the two sothat the interference sources do not cause an incorrect interpretationduring the altitude estimation (e.g., it is not interpreted as theground reflecting the airflow back).

The filter used at step 104 is a non-linear filter because linearfilters have been found to be insufficient given the complexity of thealtitude estimation problem, the complicated nature of the airflowgenerated by multiple rotors, and the non-linear dynamics of the vehicleoperating in ground effect for some types of multicopters. The altitudeestimation, generalized flow model, sensor datasets, and vehicledynamics are too complex for a linear filter to model.

In some embodiments, the non-linear filter is a non-linear Bayesianfilter. Non-linear Bayesian filters may be attractive because Bayesiantechniques are suited to work with noisy measurements, which is the casehere. Some specific non-linear Bayesian filter examples include agrid-based recursive Bayesian filter (e.g., which is attractive becauseit can be easily implemented). Other non-linear Bayesian filter examplesinclude an unscented Kalman filter or a particle filter. An advantage tousing a grid-based recursive Bayesian filter is its ability to handlenon-Gaussian measurements and dynamics (e.g., for multicopter airflow,and dealing with the interference from multiple rotors and the airframe)whereas Gaussian properties are a requirement for some non-linearfilters (e.g., unscented Kalman filter). The grid-based approach toBayesian filters also allows us to easily dictate the resolution of ourestimate by varying the grid size (where each grid represents a step inthe estimated quantity (e.g., altitude) as opposed to the complexmanipulation of particles in a particle filter) and as such can beeasily implemented with limited or constrained processing resources.

In some embodiments, the process of FIG. 1A is specifically tailored foroperations in ground effect (e.g., when the multicopter is sufficientlyclose to the ground or water that the airflow is affected by (e.g.,bends) due to the ground plane or water plane). As such, in someembodiments, the process of FIG. 1A is only performed during a verticaltakeoff or a vertical landing and/or operations close to the ground. Forexample, the process of FIG. 1A may be initiated when a vertical takeoffis imminent or begins and ends (e.g., at least temporarily) when themulticopter has reached a sufficiently high altitude that it is out ofground effect and transitions to a forward flight mode (e.g., where itflies at a constant altitude within a 2D plane). Another embodiment ofthe process in FIG. 1A may be running during the entire flight operationwhere the multicopter is always operating sufficiently close to theground or water so as to always be in ground effect. As such, theprocess in FIG. 1A is critical to estimating and maintaining thealtitude of the vehicle since any small perturbation in the vehicle'saltitude needs to be closely tracked and corrected for when close to theground or water.

FIG. 1B is a diagram illustrating an embodiment of a system whichgenerates an altitude for a multicopter. In this diagram, an examplesystem which performs the process of FIG. 1A is described. In thisexample, there are three sensors (150, 152, and 154) which output theinterference sensor dataset, the first isolated sensor dataset, and thesecond isolated sensor dataset, respectively. The datasets are passed tothe processor (156), along with a generalized flow model from storage(158). In various embodiments, the storage (memory) may be long-term orshort-term memory, volatile or non-volatile, etc. The processor (156)uses these inputs to generate an altitude for the multicopter. Forexample, the altitude may be used by the flight controller or flightcomputer to adjust and/or control the rotors of the multicopter.

It may be helpful to describe an exemplary multicopter so that theprocess of FIG. 1A can be better understood. The following figuredescribes a multicopter that is ultralight and designed to flyoverwater.

FIG. 2 is a diagram illustrating an embodiment of an ultralight andoverwater multicopter. In some embodiments, the multicopter isautonomous. In this example, the multicopter has 10 rotors (200 a and200 b). All of the rotors in this example have the same size and/ordimensions (e.g., same radius, same blade angle, same twisting, etc.).Using identical rotors (as shown here) may be helpful because thisbetter supports the use of a (e.g., single) generalized flow model (see,e.g., steps 102 and 104 in FIG. 1).

Five of the rotors are located on the port (i.e., left) side of themulticopter and the remaining five rotors are located on the starboard(i.e., right) side of the multicopter. The four outboard rotors (200 a)are positioned on the distal ends of booms (202) which extend outwardfrom the fuselage (204) and pass through the floats (206). Themulticopter is able to take off and land on water (if desired) and thefloats provide buoyancy for the multicopter to float on water. The sixinboard rotors (200 b) are positioned on the top of the float.

In this example, the multicopter is designed to fit into a trailer andtherefore the rotors are tightly packed together so that the footprintof the multicopter is sufficiently small enough to fit into a trailer.The following figure shows a top view of the multicopter with the rotorson.

FIG. 3 is a diagram illustrating a top view of a multicopter with therotors on. FIG. 3 continues the example of FIG. 2. To better show thetight packing of the rotors, the rotors in this figure are shownrotating. As shown here, there is overlap between the front inboardrotors (300) and the middle inboard rotors (302), between the middleinboard rotors (302) and the back inboard rotors (304), and between thefront outboard rotors (306) and the back outboard rotors (308). Otherparts of the multicopter also interfere with the airflow produced by therotors, such as the side of the fuselage (310) and the floats (312),both of which may affect the airflow produced by the inboard rotors(300, 302, and 304). Similarly, the booms (314) affect all rotorairflow.

In this example, sensor 320 is positioned to collect an interferencesensor dataset (e.g., received at step 100 in FIG. 1). Note, forexample, that the sensor is located beneath the edge of the (left) backoutboard rotor (308) and the (left) back inboard rotor (304) where theairflow from those two rotors will interfere with each other. Incontrast, sensors 322 a, 322 b, 322 c, 324 a, 324 b, and 324 c arepositioned to collect isolated sensor datasets. For example, thosesensors are located as far away as possible from sources ofinterference, such as other rotors or parts of the multicopter which mayinterfere with rotor airflow (e.g., away from the booms, floats, and/orfuselage). In various embodiments, the sensors may be held or otherwisepositioned at some desired position or location via a boom, rod, orother structure that is connected to various parts of the multicopter(e.g., the fuselage, a float, a (rotor) boom, etc.).

Returning briefly to FIG. 1, in some embodiments, the specific geometryof the example multicopter shown here and in FIG. 2 (e.g., the way thefloats affect airflow(s), the tight packing of the rotors, etc.) isincorporated into the process described in FIG. 1. For example, at step100 in FIG. 1, the isolated sensor datasets are collected for theoutboard rotors as opposed to the inboard rotors. In some embodiments,up to two datasets are collected per rotor for all the outboard rotors(e.g., 300, 304, 306, and 308 for the port side in FIG. 3), and only onedataset is collected for the inboard rotor (e.g., 302 in FIG. 3). Thesedatasets are located as shown in FIG. 3 by being as far away as possiblefrom the airframe, booms, floats, and other rotors. The same datasetconfiguration is repeated between the port and starboard sides due tocenterline symmetry (i.e., two datasets per outboard rotor and one perinboard rotor). Using this sensor configuration, more weight is put onthe outboard rotors which have less interference sources and canpotentially capture attitude information, and conversely, less weight isplaced on the inboard rotors which tend to have more interferencesources.

The following figure shows an example of ground effect airflow (e.g.,420 in FIG. 4) that may be sampled by sensors 320, 322 a, 322 b, 322 c,324 a, 324 b, and 324 c.

FIG. 4 is a diagram illustrating an embodiment of ground effect airflowwith induced velocity sensor datasets used as inputs to the flow model.In the example shown, the rotor on the left (400) corresponds to rotor308 from FIG. 3 and the rotor on the right (402) corresponds to rotor304 from FIG. 3. Similarly, sensors 404, 406, 416, 408, 410, 412 and 414in this example correspond to sensors 322 c, 324 c, 320, 322 a, 322 b,324 a, and 3224 b from FIG. 3, respectively. As described above, thedata from sensors 404, 406, 408, 410, 412, 414, and 416 are used tomeasure the airflow velocity for each rotor of the multicopter (100),which are used as sensor datasets in the estimation (104) of altitude(i.e., h).

Sensors 408, 410, 412 and 414 are located within the isolated airflow(420 and 422) from the rotor on the left (400) and the rotor on theright (402), respectively. In contrast, sensor 416 is located within theturbulent airflow (424 a and 424 b) where the airflow from the rotor onthe left interferes with the airflow from the rotor on the right andvice-versa. Sensors 404 and 406 are located perpendicularly close to therotor plane to measure the induced airflow velocity, which is thevelocity of the incoming airflow right below the rotor plane, which arethen input into the generalized flow model (102).

The airflow in the turbulent and/or interference regions (424 a and 424b) are flowing in the opposite direction as they normally would (e.g.,radially towards the center of the rotor or chaotically spiraling asopposed to radially away from the center of the rotor). As will bedescribed in more detail below, a generalized flow model will reflectthe expected and/or ideal direction of airflow (e.g., radially outward)and these discrepancies in directions are handled by the non-linearfilter.

In some embodiments, induced velocity sensors 404 and 406 are placed ata normalized vertical distance (e.g., below the rotor's plane ofrotation) within a range of 0.01-0.1 R (where R is the radius of therotor) and/or at a normalized radial distance (e.g., from the rotor'saxis of rotation) within a range of 0.6-0.95 R. In some applications, itis desirable to place the sensor at positions within such ranges becausethese ranges capture the induced airflow velocities as vertically closeas possible to the rotor plane and also at the radial location ofmaximum lift along the blade. In some embodiments, these ranges areoptimized for the rotor airfoil and/or local lift distribution.

In some embodiments, sensors 408, 410, 412, and 414 are placed at anormalized vertical distance within a range of 0.1-0.4 R and/or at anormalized radial distance within a range of 0.25-0.9 R. In someapplications, it is desirable to place the sensor at positions withinsuch ranges because these ranges capture the airflow velocities as theairflow is still forming and/or is fully formed but their structureshave not broken down yet or been interfered with significantly by theairflow from other rotors.

In some embodiments, sensor 416 is placed at a normalized verticaldistance within a range of 0.1-0.4 R and/or at a normalized radialdistance (e.g., from either rotor's tip) within a range of +/−0-0.2 R(where 0 R is located at the middle point between either rotor's tip).In some applications, it is desirable to place the sensor at positionswithin such ranges because these ranges capture the interference airflowvelocities between multiple rotors at approximately equal distances.

In one embodiment of the setup as shown in FIG. 4, the induced velocitysensors (404 and 406) are replaced with rotor rotational speed sensors.Instead of the induced velocity sensors which directly measure theinduced velocity at the rotor plane, the rotational speed sensorsmeasure rotor rotational speed which can be mapped to the inducedvelocity of the rotors.

In some embodiments, a sensor used to obtain the interference sensordataset and/or the isolated sensor dataset (e.g., at step 100 in FIG. 1)includes differential pressure probes. The following figures show onesuch example.

FIG. 5A is a diagram illustrating a first side view of an embodiment ofa sensor that includes differential pressure probes. In the exampleshown, there are two pairs of differential pressure probes: a pair ofradial differential pressure probes (500 and 502) and a pair of verticaldifferential pressure probes (504 a and 506 a). Each probe (500, 502,504 a, and 506 a) consists of a pipe or tube with a 90° bend where theother section of the tube, which physically connects to the pressuresensor, goes into the page (not shown here).

The radial differential pressure probe pair (500 and 502) is oriented orotherwise positioned with the openings oriented or pointing parallel tothe rotor plane. Furthermore, one of the radial probe ends (e.g., 500)needs to point radially inward and the other probe end (e.g., 502) needsto point radially outward. The vertical differential pressure probe pair(504 a and 506 a) is oriented with the openings oriented or pointingperpendicular to the rotor plane. The four probes in FIG. 5A areconnected to two differential pressure sensors, where 500 and 502connect to one sensor and measure radial pressure, and 504 a and 506 aconnect to another sensor and measure vertical pressure. These flowpressures are then converted into (e.g., calibrated) vertical and radialvelocities (e.g., using wind tunnel calibration).

FIG. 5B is a diagram illustrating a second side view of an embodiment ofa sensor that includes differential pressure probes. For clarity, theradial differential pressure probe pair (500 and 502 in FIG. 5A) is notshown to better show the vertical differential pressure probes (504 band 506 b). The view shown here is another side view with the probesrotated 90° from the view shown in FIG. 5A. From this view, the 90° bendof the differential pressure probes is more readily visible. Thesevertical probes are connected to differential pressure sensors to outputvertical (e.g., airflow) pressure, which is then calibrated intovertical velocities.

In some embodiments, the induced velocity of each rotor needs to bemeasured, e.g., in FIG. 4. For the measurement of induced velocity, avertical differential pressure probe pair is needed per rotor (see,e.g., 404 and 406 in FIG. 4). FIG. 5B is the close-up view of the 404and 406, where the vertical probes are oriented or pointed perpendicularto the rotor plane and no radial probes are needed.

A benefit to using differential pressure probes is that they are verylightweight compared to some other types of sensors. For example, it ispossible to measure altitude using lidar or radar but conventionallidar, radar, and vision-based techniques are comparatively heavy andrelatively large. In contrast, differential pressure probes havedimensions on the order of a few inches (e.g., ˜3 inches) and a weighton the order of 50 g.

Another benefit of using differential pressure probes is theirrobustness to debris and an adverse operational environment (i.e., theywork well in dusty environments or on ground surfaces with varyingreflectivity). In contrast, lidar, radar, and vision-based techniqueshave varying degrees of difficulty working robustly in theseenvironments.

More importantly, differential pressure probes work well in the presenceof ground effect (e.g., the rotor airflow generated earlier is deflectedby the ground plane and interacts with current rotor airflow, as shownin FIG. 4). In contrast, other types of altitude measurement techniquesthat rely upon other types of sensors (e.g., lidar, vision, orradar-based techniques) do not account for ground effect in theirmeasurement process and hence do not produce good altitude measurementsin the presence of ground effect. These techniques do not account forground effect explicitly, i.e., as the vehicle thrust is affected by thepresence of a ground plane (ground effect), its height changes and thesetechniques implicitly detect this height change. Conversely,differential pressure probes detect the change in thrust due to groundeffect and are hence explicitly sensing the changes, which allows forquicker estimation of height and control of the vehicle.

Yet another benefit of using differential pressure probes is theirmeasurement of the source or cause of altitude changes due to groundeffect, since a pressure change, and by association a velocity or rotorthrust change, is necessary for an aircraft to change altitude. Thischange in aircraft altitude by being in close proximity to a groundplane (i.e., without any change to motor/rotor speed) is the key effectof ground effect. By using differential pressure probes, it may bepossible to anticipate (or at least get some earlier or faster sense ofa change in altitude) compared to other distance-measuring techniques,such as lidar, vision, or radar which always measure the after-effect.

In one example the multicopter shown in FIG. 3 may have sensors assignedas follows, where one vertical-and-radial sensor comprises twodifferential pressure probe pairs (e.g., the vertical pair and theradial pair as shown in FIG. 5A) for differential pressure measurement,and one vertical sensor comprises one differential pressure probe pair(e.g., the vertical pair as shown in FIG. 5B) for induced velocitymeasurement (as input to generalized flow model 102). For brevity, thefollowing table does not differentiate between the rotors on the leftside and the right side and sensor assignment or placement is donesymmetrically.

TABLE 1 Example Sensor Assignment Number of Induced Velocity Number ofSensors (2 DPP Pairs, Sensors (1 Vertical DPP Rotor FIG. 5A) BeneathRotor Pair, FIG. 5B) Beneath Rotor Front Inboard Rotor (e.g., 300 2(away from interference sources) 1 in FIG. 3) Middle Inboard Rotor(e.g., 302 1 (farthest location from airframe) 1 in FIG. 3) Back InboardRotor (e.g., 304 2 (e.g., 324a and 324b in FIG. 3) 1 (e.g., 324c in FIG.3) in FIG. 3) Front Outboard Rotor (e.g., 306 2 1 in FIG. 3) BetweenBack Outboard Rotor 1 (e.g., 320 in FIG. 3) 0 (e.g., 308 in FIG. 3) andBack Inboard Rotor (e.g., 304 in FIG. 3) Back Outboard Rotor (e.g., 3082 (e.g., 322a and 322b in FIG. 3) 1 (e.g., 322c in FIG. 3) in FIG. 3)

In this example, the middle inboard rotors (e.g., 302 in FIG. 3) arecompletely surrounded by other rotors, as well as the sidewall of thefuselage. As a result, the airflow produced by the middle inboard rotorsis more turbulent and has more interference compared to the airflowproduced by the other rotors. As such, in this example, there is onlyone sensor (e.g., like that shown in FIG. 5A) and one induced velocitysensor (e.g., like that shown in FIG. 5B) placed beneath the middleinboard rotor because less weight is placed on locations known toproduce noisier and lower quality sensor data. In the context of FIG. 1,for example, the plurality of sensor datasets (e.g., received at step100) would have less sensor data associated with (e.g., sampled from) arotor that is surrounded (e.g., by a plurality of rotors, the fuselage,and/or other parts of the multicopter) such that the altitude generated(e.g., at step 104) would place less weight on the sensor data from thesurrounded rotor and place more weight on other rotors. In someembodiments, the surrounded rotor (e.g., with the sensor data carryingless weight in the altitude estimation or generation) overlaps with atleast one other rotor (e.g., which makes the airflow beneath thesurrounded rotor even more messy or chaotic).

Another example sensor assignment is similar to the example shown inTable 1, except that rotor rotational speed sensors (e.g., Hall effectsensors) can be used instead of one vertical sensor (see, e.g., FIG. 5B)for induced velocity measurement per rotor. This can be achieved bycalibrating the rotor rotational speed to correlate with the rotorinduced velocity. In this example, Table 1 would have its right-mostcolumn replaced with a rotational speed sensor per rotor. The advantageof this example is that most rotor and/or motor speed controllerstypically have such a sensor and can be repurposed to reduce the numberof components, interference between probes and rotors, weight, and cost.

The following figure shows an example airflow associated with ageneralized flow model.

FIG. 6A is a three-dimensional graph illustrating an embodiment of ageneralized flow model with the rotor at a first height. In the exampleshown, the rotor (600 a) is at a normalized height of h=1R where the his the height of the rotor above the ground plane (602 a) and R is theradius of the rotor. The graph also includes various flow lines (604 a)showing the direction of airflow (e.g., initially down towards theground plane before turning and running parallel to the ground plane).It is noted that the generalized flow model is associated with a singlecomposite rotor made up of all rotors in the multicopter. There is noseparate model of how two or more adjacent rotors affect each other'sairflow, but rather this generalized flow model combines all rotors forthe multicopter and models the airflow as one large composite rotor. Theinterference between each rotor is modeled internally within thegeneralized model as local disturbances.

Another feature of the generalized flow model is the modeling of themulticopter airframe at the centerline as a “rotor hub,” which reducesthe effective thrust-generating area and hence reduces the amount ofthrust that can be generated.

One benefit of this generalized rotor modeling approach is that lessmemory and computation is required for a generalized flow model withlocal disturbances (i.e., inter-rotor interference) as opposed to havingmultiple rotor models, inter-rotor interference models, and asummarizing model to mimic the behavior of the vehicle as a function ofall these other models.

Another benefit of modeling the airframe as the effective rotor hub forthis generalized flow model is we use prior knowledge of significantinterference factors, such as the airframe, to account for significantinterference and loss of effective thrust-generating area, which doesnot overestimate the effect of the ground plane or amount of thrustgenerated. This modeling approach allows for more accurate estimation ofaltitude by closely modeling the actual thrust generated.

FIG. 6B is a two-dimensional graph illustrating an embodiment of ageneralized flow model with the rotor at a first height. FIG. 6B is thetwo-dimensional version of the three-dimensional graph shown in FIG. 6A.Note, for example, that both are at a normalized height of h=1R. Rotor600 b, ground plane 602 b, and flow lines 604 b correspond to rotor 600a, ground plane 602 a, and flow lines 604 a from FIG. 6A.

FIG. 6C is a two-dimensional graph illustrating an embodiment of ageneralized flow model with the rotor at a second height. In thisexample, the rotor (600 c) is at a normalized height of h=2R. Theresulting flow lines (604 c) are shown as the airflow bends away fromground plane 602 c. Contrasting FIG. 6B with FIG. 6C, we can see thatthe rotor airflow streamlines (indicated by the lines such as 604 c)have smaller radii of curvature (i.e., bend more) when the rotor iscloser to the ground at FIG. 6B, which corresponds to higher rotor flowspeed close to the ground, as shown by the speed colormap. Thisphenomenon where rotor flow speed is higher as the rotor gets closer tothe ground, and hence ground effect is stronger, is analogous to makingwater (rotor airflow) flow faster by pushing a hose (rotor plane) closerto the ground and corresponds well with reality

The above figures show the (e.g., scalar) speed at a given point for agiven height of the rotor and for a given induced velocity (e.g., thevertical velocity of the induced airflow above the rotor (not shown) asit enters or otherwise approaches the rotor; this induced velocityvaries with rotor speed).

To obtain the colormap representative of the speed for each point,∥V∥=√{square root over (υ²+ω²)} where ∥V∥ is the (scalar) speed, υ isthe vertical velocity for a given point in space (e.g., which ismeasured by vertical DPP pair 504 a and 506 a in FIG. 5A), and ω is theradial velocity for a given point in space (e.g., which is measured byradial DPP pair 500 and 502 in FIG. 5A).

In other words, the flow model for one rotor is obtained by taking theinduced velocity (or rotor rotational speed alternatively) as an inputto the model and sweeping a range of rotor heights to obtain verticalvelocities and radial velocities at various points or locations in space(e.g., below the rotor). The following table shows this:

TABLE 2 Example of Flow Model for a Single Rotor Rotor at Height 1 . . .Rotor at Height N Induced Velocity Vertical velocities (υ) & radial . .. Vertical velocities (υ) & radial as Input (e.g., at velocities (ω) atvarious velocities (ω) at various Rotor Speed 1) points/locations in 3Dspace points/locations in 3D space

The generalized flow model is obtained by taking the induced velocities(or rotor rotational speeds alternatively) of all ten rotors as input tothe model and sweeping a range of rotor heights to obtain verticalvelocities and radial velocities at various points or locations in space(e.g., below the generalized composite rotor plane).

TABLE 3 Example of Flow Model for a Generalized Composite Rotor Rotor atHeight 1 . . . Rotor at Height N Induced Velocity 1 Vertical velocities(υ) & radial . . . Vertical velocities (υ) & radial as Input (e.g., atvelocities (ω) at various velocities (ω) at various Rotor 1)points/locations in 3D space points/locations in 3D space . . . . . . .. . . . . Induced Velocity M Vertical velocities (υ) & radial . . .Vertical velocities (υ) & radial as Input (e.g., at velocities (ω) atvarious velocities (ω) at various Rotor 10) points/locations in 3D spacepoints/locations in 3D space

In one embodiment, for compactness and/or to utilize storage moreefficiently, the generalized flow model is computed and stored using(taking advantage of) the vehicle's symmetry. When we know that theaircraft is approximately level, that is, roll and pitch angles areclose to zero (e.g., by feeding in attitude data from the aircraftestimator and comparing it to an attitude threshold that is close tozero), we can assume that the rotor thrust generated is approximatelysimilar along the airframe centerline (i.e., the longitudinal axis ofsymmetry separating port and starboard side). Using this insight, onlyhalf the generalized flow model (separated by the airframe centerline,e.g., port side) has to be stored and computed, where the other half(e.g., starboard side) is assumed to mirror the half that was computed.Due to this insight, the estimation step only needs to incorporate halfof the sensor data with half of the flow model being computed, whichfurther improves the storage and computational efficiency. Naturally, ifthe vehicle should begin to tilt so that it is no longer level (e.g.,the attitude exceeds the attitude threshold), it may be desirable tocompute the entire generalized flow model. In some embodiments, theprocessor may periodically compute the entire generalized flow model(e.g., even if the attitude threshold is not exceeded) to help ensurethat the generalized flow model remains accurate.

In another embodiment, the generalized flow model can be furtheroptimized for storage and computation efficiency when the vehicle isapproximately level, by computing and hence storing only a quarter ofthe generalized flow model, i.e., not only assuming symmetricity forhalf of the model separated along the airframe centerline and/orlongitudinal axis of symmetry, but also along the non-symmetricallatitudinal axis (which separates the “fore” and “aft” of the airframe).Similarly, the estimation step would only need to be stored and computedusing a quarter of the sensor datasets and flow model. It is of notethat this optimization method should be used sparingly with the fullflow model computation, e.g., toggling between quarter and full flowmodel computation between successive estimation iterations, or quarter,half and then full flow model computation between successive estimationiterations, to account for other disturbances and noise.

Returning briefly to step 104 in FIG. 1, in some embodiments, theconsolidated probability function is continually updated by thenon-linear filter (e.g., throughout the multicopter's flight). Thefollowing figures show an example of this.

FIG. 7A is a graph illustrating an embodiment of a consolidatedprobability function, comprising a prior probability density function,at a first point in time. As described above, the consolidatedprobability function (700 a) is called a consolidated function becauseit consolidates information from multiple rotors, each of which may havemultiple sensor datasets.

FIG. 7B is a graph illustrating an embodiment of a likelihood functionwhich is constructed using sensor data and the generalized flow model.In this example, the sensor data (e.g., associated with a current timeof t or current index or iteration i) from the rotors is used toconstruct likelihood function 702 b, for example, in combination withthe generalized flow model. Conceptually, likelihood function 702 bestimates a corresponding probability for each height or altitude in arange of altitudes by comparing the difference between the sensor dataand the generalized flow model at different altitudes (e.g., withouttaking prior function (700 b) into account). Since the generalized flowmodel can be probed at any radial and vertical locations, each sensordataset is compared with its location-specific flow model output. Thesmallest difference between the data and the model yields the highestprobability at that specific altitude. Since the generalized flow modelmodels the various interference sources and aircraft geometry, it iscapable of compensating for the unsteady airflow the sensor datasetsmeasure.

FIG. 7C is a graph illustrating an embodiment of a posterior functionwhich is constructed from a likelihood function and a prior function. Inthis example, the prior function (700 c) is combined with the likelihoodfunction (702 c) using non-linear Bayesian techniques to obtainposterior function (704 c). From this posterior function, the altitudeor height (i.e., h_(output)) associated with the maxima (706) is outputas the (e.g., estimated or measured) altitude or height for themulticopter (e.g., at step 104 in FIG. 1).

In some embodiments, while a multicopter is on the ground and/or at thebeginning of a takeoff, instead of constructing posterior function 704 cand using that to estimate altitude, an (initial) probability densityfunction is used where the probability at a height or altitude of 0 isat or near 100% probability (e.g., because it is known when the altitudeestimation process starts that the multicopter is definitely on theground).

FIG. 7D is a graph illustrating an embodiment of a predicted function.At this step, posterior function 704 d is updated to generate aprediction (708). For example, since this application relates toaltitude estimation, any estimated and/or known information associatedwith ascending, descending, or staying at a same altitude (e.g., climbvelocity) may be used to shift the prior function (i.e., shifting theprobability mass) so that the peak moves leftward (e.g., descending),rightward (e.g., ascending), or generally the same (e.g., staying at aconstant altitude). The shifted probability mass 708 is then diffusedwith process noise. That is, the uncertainty related to the processand/or motion model lowers the probability (i.e., lowers the confidenceof the estimation output to deal with motion uncertainty) to produce thepredicted function 710. Finally, the predicted function 710 is set asthe prior function 700 a for the next time step or iteration.

The following figure describes this example more generally and/orformally in a flowchart.

FIG. 8 is a diagram illustrating an embodiment of a process to generatean altitude for a multicopter where a consolidated probability functionis updated over time. FIG. 8 is related to FIG. 1A and for conveniencerelated steps are indicated using the same or similar reference numbers.

At 100, a plurality of sensor datasets including: (1) an interferencesensor dataset which is associated with interference between airflowfrom a first rotor in a multicopter and airflow from a second rotor inthe multicopter, (2) a first and a second isolated sensor dataset whichare associated with isolated airflow from the first rotor and the secondrotor, respectively, is received.

At 102, a generalized flow model associated with a generalized rotor(e.g., a composite rotor model comprised of multi-rotors) is received.

At 104′, an altitude for the multicopter is generated based at least inpart on the plurality of sensor datasets and the generalized flow model,including by: using a non-linear filter that builds a consolidatedprobability function associated with altitude that reconciles theplurality of sensor datasets with the generalized flow model; andinitializing the consolidated probability function to be a probabilityfunction associated with being on the ground. For example, the altitudeestimation process (shown here) will typically begin before takeoffoccurs and when the aircraft is still on the ground. As such, theprobability function can be initialized to a probability (distribution)function where the probability is highly and/or completely skewedtowards an altitude of zero (i.e., being on the ground). Initializingthe probability function in this manner may be helpful because it startsthe altitude estimation process out with an accurate probabilityfunction and helps the process start with accurate altitudes.

At 802, it is decided whether to end the process. For example, thealtitude estimation may run throughout the flight and end only after theaircraft has landed.

If it is decided not to end the process, then at 804, the consolidatedprobability function is updated based at least in part on a directionand rate of altitude change, if any. For example, posterior function 704d in FIG. 7D is updated based on whether the aircraft ascends, descends,or stays at the same altitude and diffused to become prediction function710. In some embodiments, this direction and rate (velocity) of altitudechange, if any, is determined by tracking the altitudes that aregenerated. Prediction function 710 then becomes the consolidatedprobability function which is used at the next iteration (700 a) togenerate the next altitude.

The process then goes through another iteration or pass (e.g., togenerate the next altitude estimate or measurement) by receiving anotherplurality of sensor datasets at 100 (e.g., with new sensor data).

Returning briefly to FIG. 1, in some embodiments, other measurements orestimates are generated in addition to the altitude at step 104. Thefollowing figure shows an example of this.

FIG. 9 is a diagram illustrating an embodiment of a process to generatean altitude and an attitude for a multicopter. FIG. 9 is related to FIG.1A and for convenience related steps are indicated using the same orsimilar reference numbers. This technique may be combined with any ofthe other techniques described herein; specific combinations of varioustechniques are not necessarily described for brevity.

At 100, a plurality of sensor datasets including: (1) an interferencesensor dataset which is associated with interference between airflowfrom a first rotor in a multicopter and airflow from a second rotor inthe multicopter, (2) a first and a second isolated sensor dataset whichare associated with isolated airflow from the first rotor and the secondrotor, respectively, is received.

At 102, a generalized flow model associated with a generalized rotor isreceived. Since the generalized flow model is a composite rotor modelcomprised of multiple rotors, inherently the model is capable ofsimulating rotor airflow generated by a vehicle flying at non-levelattitudes by adding a few parameters. To be used for attitudeestimation, the generalized flow model needs to incorporate both rolland pitch angles as parameters such that the airflow can be generatedfor non-zero attitudes. In one example, if the vehicle is pitchedforward (fore section tilting downward), the airflow speed generated isfaster in the fore section as opposed to the aft section, which iscaptured by the generalized flow model.

At 104″, an altitude and an attitude for the multicopter are generatedbased at least in part on the plurality of sensor datasets and thegeneralized flow model, including by using a non-linear filter thatbuilds a consolidated probability function associated with altitude andaltitude that reconciles the plurality of sensor datasets with thegeneralized flow model. The following figure shows an example of tworotors with a non-zero attitude and may be helpful to illustrate howstep 104″ is performed.

FIG. 10 is a diagram illustrating an embodiment of ground effect airflowwhen there is a non-zero attitude. For simplicity and ease ofexplanation, two rotors (1000 and 1002) are used to represent an entiremulticopter with multiple rotors (e.g., the multicopter shown in FIGS. 2and 3). Also for simplicity and ease of explanation, the interferencebetween the two airflows generated by the two rotors is not shown in thediagram.

When a multicopter is not level (as is shown here), the attitude (e.g.,comprising a roll and pitch value) will be non-zero. The attitude can beestimated by the different measurements of the sensor datasets. Forexample, sensor 1004 (which is located beneath the rotor (1000) that iscloser to the ground plane) will tend to observe higher airflowvelocities (due to the airflow bouncing off the closer ground plane)compared to sensor 1006 (which is located beneath the rotor (1002) thatis located further from the ground plane). This difference in rotorairflow velocities can be translated or otherwise used to generate(e.g., estimate of) the multicopter's attitude. Note that although onlytwo sensors (1004 and 1006) are shown for simplicity, the actual numberof sensors is similar to those shown in Table 1.

More specifically, the sensor datasets are first collected. Note thatthe numbers of sensors and sensor locations are the same for theestimation of altitude and attitude. The generalized flow model withattitude parameters to tilt the airflow is then updated within theestimation step. Similar to altitude estimation, the non-linearestimator compares the difference between the sensor speeds and the flowmodel speeds in order to update the consolidated probability function,where the smallest difference between sensor and model values yields thehighest probability.

The estimation framework is tightly coupled between the altitude andattitude estimation for the exemplary vehicle described herein, whichmeans that altitude and attitude are not separately and/or individuallyestimated. This tightly coupled estimation framework choice is so chosensince the Flyer attitude and altitude are closely related. For example,as the Flyer pitches forward and/or nose-down, it loses altitudesimultaneously since the same rotors that provide pitch control alsoprovide altitude control. A counter-example to this would be athrust-vectoring capable vehicle where altitude and attitude controlsare separate.

Specifically, the consolidated probability function for estimating bothaltitude, and roll angle and pitch angle (known together as attitude) isexpanded to be a four-dimensional probability function, three dimensionsfor each estimated parameter and one dimension for the probability. Theconsolidated probability function is updated sequentially along eachdimension, i.e., in a tightly-coupled fashion, and upon completion ofthis step, all three estimates for altitude, roll angle, and pitch angleare produced.

Similar to the case of altitude estimation using half or a quarter ofthe flow-model when the vehicle is approximately level, altitude andattitude estimation can also be further optimized to use only half or aquarter of the flow model since the assumption of symmetricity of rotorairflow along both longitudinal and latitudinal vehicle axes holds truefor level attitude. This assumption of symmetricity is motivated by thegeometry of the exemplary 10-rotor multicopter vehicle (described above)which has exactly the same number of rotors on its left-right andfore-aft sides, which is suitably modeled by the generalized compositeflow model comprised of multiple rotors. Using these optimizations, onlyhalf or a quarter of the flow model and estimation step comparing sensordatasets and flow models have to be computed and stored.

The fact that this attitude estimation framework can help determine theuse of the half or quarter-model optimization (i.e., only duringapproximately level attitudes) makes this altitude and attitudeestimation framework a self-containing/standalone system which does notrequire other sensing modalities and estimation frameworks.

The half or quarter-flow models should be sparingly used with the fullflow model computations especially for altitude and attitude estimation,e.g., using a half or quarter-flow model and then using a full flowmodel between successive estimation iterations to ensure thatdisturbances and noise do not creep into the estimation too quickly.

While the half and quarter-flow models and estimation optimizations canbe used for approximately level attitude, in the case of large attitudeangles, the full flow model and estimation framework have to be used. Inone example where the exemplary vehicle described above is limited tooperate up to certain attitudes, further optimizations are done tostrike a balance between accurate estimation and decreased computationand storage requirements. In one example, between 0-5 degrees of roll orpitch, a quarter-flow model and estimation optimization is used thenfollowed by a half-model optimization and then a full-model computationbetween successive estimation iterations; between 5-8 degrees of roll orpitch, a half-model optimization is used and then a full-modelcomputation between successive estimation iterations; larger than 8degrees of roll or pitch, only full-model computations are allowed.

Another consideration specific to the exemplary vehicle described aboveis that at altitudes less than 0.75 effective rotor radius (i.e.,three-quarters of half of the maximum tip-to-tip distance between theoutboard rotors), i.e., during takeoff and landing which tend to haverapidly-changing non-level attitude and significant airflow turbulencedue to the pontoon and booms being in the rotor wake, the half andquarter-flow model optimizations are not used. Between altitudes of0.75-1.25 effective rotor radius, the half-model optimization is usedand then the full model computation between successive estimationiterations. At 1.25-2.0 effective rotor radius, the quarter-modeloptimization is used, followed by the half-model optimization and thenthe full model computation between successive estimation iterations.

Although the foregoing embodiments have been described in some detailfor purposes of clarity of understanding, the invention is not limitedto the details provided. There are many alternative ways of implementingthe invention. The disclosed embodiments are illustrative and notrestrictive.

What is claimed is:
 1. (canceled)
 2. A system, comprising: a processor;and a memory coupled with the processor, wherein the memory isconfigured to provide the processor with instructions which whenexecuted cause the processor to: receive an interference sensor datasetassociated with interference between airflows from at least two rotorsin a multicopter and a first isolated sensor dataset and a secondisolated sensor dataset which are associated with isolated airflows froma first rotor and a second rotor in the multicopter, respectively;receive a generalized flow model associated with a generalized rotor;and generate an altitude for the multicopter based at least in part onthe interference sensor dataset, the first isolated sensor dataset, thesecond isolated sensor dataset, and the generalized flow model,including by using a non-linear filter that builds a consolidatedprobability function associated with altitude that reconciles theinterference sensor dataset, the first isolated sensor dataset, and thesecond isolated sensor dataset with the generalized flow model.
 3. Thesystem recited in claim 2, wherein the interference sensor dataset isobtained from a sensor that is placed beneath at least two overlappingrotors in the multicopter.
 4. The system recited in claim 2, wherein theinterference sensor dataset is used to separate multi-rotor interferencefrom ground effect.
 5. The system recited in claim 2, wherein: themulticopter includes an ultralight, open-cockpit vehicle with at leastone float; and at least one rotor is coupled to a top surface of said atleast one float.
 6. The system recited in claim 2, wherein: themulticopter includes an middle inboard rotor that is surrounded by afuselage and a plurality of other rotors; and more isolated sensordatasets are collected per rotor from the plurality of other rotors thanfrom the middle inboard rotor.
 7. The system recited in claim 2, whereinat least one of the interference sensor dataset, the first isolatedsensor dataset, or the second isolated sensor dataset is obtained usingdifferential pressure probes.
 8. The system recited in claim 2, whereingenerating the altitude for the multicopter further includes generatingan attitude for the multicopter.
 9. The system recited in claim 2,wherein: generating the altitude for the multicopter further includesgenerating an attitude for the multicopter; and the altitude and theattitude are generated simultaneously, including by using afour-dimensional consolidated probability function associated withaltitude, roll angle, and pitch angle.
 10. A method, comprising:receiving an interference sensor dataset associated with interferencebetween airflows from at least two rotors in a multicopter and a firstisolated sensor dataset and a second isolated sensor dataset which areassociated with isolated airflows from a first rotor and a second rotorin the multicopter, respectively; receiving a generalized flow modelassociated with a generalized rotor; and generating an altitude for themulticopter based at least in part on the interference sensor dataset,the first isolated sensor dataset, the second isolated sensor dataset,and the generalized flow model, including by using a non-linear filterthat builds a consolidated probability function associated with altitudethat reconciles the interference sensor dataset, the first isolatedsensor dataset, and the second isolated sensor dataset with thegeneralized flow model.
 11. The method recited in claim 10, wherein theinterference sensor dataset is obtained from a sensor that is placedbeneath at least two overlapping rotors in the multicopter.
 12. Themethod recited in claim 10, wherein the interference sensor dataset isused to separate multi-rotor interference from ground effect.
 13. Themethod recited in claim 10, wherein: the multicopter includes anultralight, open-cockpit vehicle with at least one float; and at leastone rotor is coupled to a top surface of said at least one float. 14.The method recited in claim 10, wherein: the multicopter includes anmiddle inboard rotor that is surrounded by a fuselage and a plurality ofother rotors; and more isolated sensor datasets are collected per rotorfrom the plurality of other rotors than from the middle inboard rotor.15. The method recited in claim 10, wherein at least one of theinterference sensor dataset, the first isolated sensor dataset, or thesecond isolated sensor dataset is obtained using differential pressureprobes.
 16. The method recited in claim 10, wherein generating thealtitude for the multicopter further includes generating an attitude forthe multicopter.
 17. The method recited in claim 10, wherein: generatingthe altitude for the multicopter further includes generating an attitudefor the multicopter; and the altitude and the attitude are generatedsimultaneously, including by using a four-dimensional consolidatedprobability function associated with altitude, roll angle, and pitchangle.
 18. A computer program product, the computer program productbeing embodied in a non-transitory computer readable storage medium andcomprising computer instructions for: receiving an interference sensordataset associated with interference between airflows from at least tworotors in a multicopter and a first isolated sensor dataset and a secondisolated sensor dataset which are associated with isolated airflows froma first rotor and a second rotor in the multicopter, respectively;receiving a generalized flow model associated with a generalized rotor;and generating an altitude for the multicopter based at least in part onthe interference sensor dataset, the first isolated sensor dataset, thesecond isolated sensor dataset, and the generalized flow model,including by using a non-linear filter that builds a consolidatedprobability function associated with altitude that reconciles theinterference sensor dataset, the first isolated sensor dataset, and thesecond isolated sensor dataset with the generalized flow model.
 19. Themethod recited in claim 10, wherein: the multicopter includes anultralight, open-cockpit vehicle with at least one float; and at leastone rotor is coupled to a top surface of said at least one float. 20.The computer program product recited in claim 18, wherein: themulticopter includes an middle inboard rotor that is surrounded by afuselage and a plurality of other rotors; and more isolated sensordatasets are collected per rotor from the plurality of other rotors thanfrom the middle inboard rotor.
 21. The computer program product recitedin claim 18, wherein: the computer instructions for generating thealtitude for the multicopter further include computer instructions forgenerating an attitude for the multicopter; and the altitude and theattitude are generated simultaneously, including by using afour-dimensional consolidated probability function associated withaltitude, roll angle, and pitch angle.